Boubacar Mainassara, Yacouba (2009): Multivariate portmanteau test for structural VARMA models with uncorrelated but nonindependent error terms.
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Abstract
We consider portmanteau tests for testing the adequacy of structural vector autoregressive movingaverage (VARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. The structural forms are mainly used in econometrics to introduce instantaneous relationships between economic variables. We first study the joint distribution of the quasimaximum likelihood estimator (QMLE) and the noise empirical autocovariances. We then derive the asymptotic distribution of residual empirical autocovariances and autocorrelations under weak assumptions on the noise. We deduce the asymptotic distribution of the LjungBox (or BoxPierce) portmanteau statistics in this framework. It is shown that the asymptotic distribution of the portmanteau tests is that of a weighted sum of independent chisquared random variables, which can be quite different from the usual chisquared approximation used under independent and identically distributed (iid) assumptions on the noise. Hence we propose a method to adjust the critical values of the portmanteau tests. Monte carlo experiments illustrate the finite sample performance of the modified portmanteau test.
Item Type:  MPRA Paper 

Original Title:  Multivariate portmanteau test for structural VARMA models with uncorrelated but nonindependent error terms 
Language:  English 
Keywords:  Goodnessoffit test, QMLE/LSE, BoxPierce and LjungBox portmanteau tests, residual autocorrelation, Structural representation, weak VARMA models 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  27637 
Depositing User:  Boubacar Mainassara Yacouba 
Date Deposited:  19 Jan 2011 12:34 
Last Modified:  01 Oct 2019 05:16 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/27637 
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Multivariate portmanteau test for structural VARMA models with uncorrelated but nonindependent error terms. (deposited 08 Dec 2009 23:39)

Multivariate portmanteau test for structural VARMA models with uncorrelated but nonindependent error terms. (deposited 18 Jun 2010 22:15)
 Multivariate portmanteau test for structural VARMA models with uncorrelated but nonindependent error terms. (deposited 19 Jan 2011 12:34) [Currently Displayed]

Multivariate portmanteau test for structural VARMA models with uncorrelated but nonindependent error terms. (deposited 18 Jun 2010 22:15)